isRetrocompact_zeroLocus_compl_of_fg

English

If I is a finitely generated ideal of R, then the complement of the zero locus of I is retrocompact in Spec(R).

Русский

Если I — FG-идеал R, дополнение к нульт локусу Iretrocompact.

LaTeX

$$$$ I \text{ FG} \Rightarrow IsRetrocompact(\operatorname{zeroLocus}(I))^{c}. $$$$

Lean4

theorem isRetrocompact_zeroLocus_compl_of_fg {I : Ideal R} (hI : I.FG) : IsRetrocompact (zeroLocus (I : Set R))ᶜ :=
  by
  obtain ⟨s, rfl⟩ := hI
  rw [zeroLocus_span]
  exact isRetrocompact_zeroLocus_compl s.finite_toSet

Похожие утверждения